Lattice Symmetry‐Guided Charge Transport in 2D Supramolecular Polymers Promotes Triplet Formation

Abstract Singlet‐to‐triplet intersystem crossing (ISC) in organic molecules is intimately connected with their geometries: by modifying the molecular shape, symmetry selection rules pertaining to spin‐orbit coupling can be partially relieved, leading to extra matrix elements for increased ISC. As an analog to this molecular design concept, the study finds that the lattice symmetry of supramolecular polymers also defines their triplet formation efficiencies. A supramolecular polymer self‐assembled from weakly interacting molecules is considered. Its 2D oblique unit cell effectively renders it as a coplanar array of 1D molecular columns weakly bound to each other. Using momentum‐resolved photoluminescence imaging in combination with Monte Carlo simulations, the study found that photogenerated charge carriers in the supramolecular polymer predominantly recombine as spin‐uncorrelated carrier pairs through inter‐column charge transfer states. This lattice‐defined recombination pathway leads to a substantial triplet formation efficiency (≈60%) in the supramolecular polymer. These findings suggest that lattice symmetry of micro‐/macroscopic structures relying on intermolecular interactions can be strategized for controlled triplet formation.


S1. Simulations of back-focal-plane images
The formulism used for the simulations in this study were based on those developed by Schuller et al. 1 In principle, we consider a three-layer system including air (layer 1, refractive index n1 = 1), supramolecule structures (layer 2, refractive index n2 = 1.78), and immersion oil on substrate (layer 3, refractive index n3 = 1.52) (Fig. S1).We assign the a-and b-axes of the supramolecule nanoribbons to be the x-and y-directions of the sample plane, and the direction perpendicular to the nanoribbon surface the z-or out-of-plane (OP) direction.For a nanoribbon with an overall emission transition dipole moment µ, whose dipole strength along the x (a), y (b), and z (OP) directions are |µa| 2 , |µb| 2 , and |µOP| 2 , its spontaneous decay rate (Γ) at electromagnetic frequency  can be derived using the Fermi's golden rule: [1][2][3]   with  being a constant related to the measurement condition.
The analytical expressions for the normalized local density of optical states, ρ ̃=,,OP , (,  ‖ ), can be derived using the reciprocity theorem: Here, d is the thickness of the supramolecular nanoribbon,   is the refractive index in layer i,   , and   , represent  and  polarized transition (t) or reflection (r) coefficients from layer i to layer j:  Fitting results are listed in the table below.

S3. Estimation of recombination pathways
If we assume that in a given time, the number of photons emitted by the Frenkel exciton state is n0, based on the transition dipole ratios determined from the BFP studies (|µa| 2 : |µb| 2 : |µOP| 2 = 6.0 : 11.6 : 1.0), we can derive that photons emitted through the 1 CTintra state and 1 CTinter state are 6n0 and 12n0, respectively.Because quantum yield of the PMI molecule is close to unity, 4 we can assume that the 1 S1 → 1 S0 recombination occurs predominantly radiatively with negligible nonradiative processes.However, quantum yields of the 1 CTintra and 1 CTinter states are prior unknown.We define them as 1 QYintra = 6n0/(6n0 + nb) and 1 QYinter = 12n0/(12n0 + na), respectively, with nb and na being the corresponding numbers of carrier pairs recombined nonradiatively.For simplicity, we assume nb ≈ na because of the long lifetimes of the 1 CTintra and 1 CTinter states.Since the 1 CTinter and 3 CTinter states are populated in a 1:3 ratio, we can determine that populations of carrier pairs recombined through the 3 CTinter state is 3(12n0 + na), most of which would relax to the molecular triplets or recombine nonradiatively.
The supramolecular nanoribbons have an overall quantum yield of ~ 1%. 5 We can thus derive that percentages of charge carriers that recombine through the 1 S1, 1 CTintra, 1 CTinter and 1 CTinter states to be 0.05%, 20%, 20%, and 60%, respectively.Due to the lack of previously reported ∆ values for this system, the values adapted here are mostly relative values between the Frenkel excitons and charge carriers based on their respective matrix elements that facilitate their hopping to neighbors. 9Rectangular barriers are considered and the WKB approximation is used.

Figure S1 .
Figure S1.Side-view of the three-layer structure used in the simulation.

Amplitude 1 Figure
Figure S5.(a) Transient absorption spectra at selected pump-probe delays of nanoribbons upon 440 nm femtosecond laser excitation.(b) Decay spectra obtained by an SVD analysis.

Figure S6 .
Figure S6.Energy levels and carrier populations involved in the estimation.Solid and dashed red arrows represent radiative and nonradiative recombination, respectively.

Figure S7 .
Figure S7.Sketch of the optical microscope used for real-space and BFP imaging and spectroscopy.BPF: band-pass filter; HWP: half-wave plate; BS: beam splitter; LPF: long-pass filter.The lenses with dashed lines are removable, allowing a switching between the realspace and BFP imaging mode.